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In the given experiment, a die is rolled.
Let, E be the event “the die shows 4”.So set E contains the element 4.
E={ 4 }
Let, F be the event that die shows even number”. So set F contains all the even numbers from 1 to 6.
F={ 2,4,6 }
Two events, A and B are mutually exclusive if, A∩B=ϕ.
E∩F={ 4 }∩{ 2,4,6 } =4 .
It can be observed that E∩F≠ϕ.
Thus, E and F are not mutually exclusive.
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Now, let's delve into your question. You've mentioned two events: E, which is the event "die shows 4," and F, the event "die shows an even number."
In probability theory, events are mutually exclusive if they cannot both occur at the same time. In this case, event E and event F are not mutually exclusive. Why? Because rolling a 4 satisfies both conditions: it is an even number (thus satisfying event F) and it is specifically a 4 (satisfying event E).
So, in conclusion, E and F are not mutually exclusive since there exists an outcome (rolling a 4) that satisfies both events simultaneously. If you have any further questions or need clarification, feel free to ask! And remember, UrbanPro is your go-to platform for all your educational needs.
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